Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}6x-y &= -3 \\ -6x-y &= -9\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-y = 6x-9$ Divide both sides by $-1$ to isolate $y$ $y = {-6x + 9}$ Substitute this expression for $y$ in the first equation. $6x-({-6x + 9}) = -3$ $6x + 6x - 9 = -3$ Simplify by combining terms, then solve for $x$ $12x - 9 = -3$ $12x = 6$ $x = \dfrac{1}{2}$ Substitute $\dfrac{1}{2}$ for $x$ back into the top equation. $6( \dfrac{1}{2})-y = -3$ $3-y = -3$ $-y = -6$ $y = 6$ The solution is $\enspace x = \dfrac{1}{2}, \enspace y = 6$.